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Our present contribution sets out to investigate how combined effects of Lorentz-symmetry violation (LSV) and Loop-Quantum-Gravity(LQG)-modified photon dispersion relations affect the threshold anomaly of cosmic photons. The point of departure is the post-Maxwellian version of Electromagnetism induced by LQG effects. We then consider the problem of gamma-ray attenuation by the Extragalactic Background Light (EBL) and the Cosmic Microwave Background Radiation (CMB) dominated by the Breit-Wheeler Effect. By following this path, we aim at the establishment of a new bridge between LSV and astrophysical phenomena in the framework of LQG., Comment: 7 pages, 2 figures

Our present contribution sets out to investigate a scenario based on the effects of the Loop Quantum Gravity (LQG) on the electromagnetic sector of the Standard Model of Fundamental Interactions and Particle Physics (SM). Starting then from a post-Maxwellian version of Electromagnetism that includes LQG effects, we work out and discuss the influence of LQG parameters on classical quantities, such as the components of the stress-tensor. Furthermore, we inspect the propagation of electromagnetic waves and study optical properties of the QED vacuum in this scenario. Among these, we contemplate the combined effect between the LQG parameters and a homogeneous background magnetic field on the propagation of electromagnetic waves, considering in detail issues like group velocities and refractive indices of the QED vacuum. Finally, with the help of the LQG-extended photonic dispersion relations previously analyzed, we re-discuss the kinematics of the Compton effect and conclude that there emerges an interesting nonlinear profile in the wavelengths of both the incoming and the deflected photons., Comment: 9 pages, 0 figures

We examine the effects of electromagnetic field non-linearities in $3$ space-time dimensions. We focus on how these non-linearities influence permittivity and susceptibility. This, in turn, leads to changes in the refractive index through the use of the dispersion relation in the context of massless and massive non-linear electrodynamics. We also verify that, by inspecting the model addressed in the frequency/wave vector space, we identify the characteristics of a non-local material in the behavior of the vacuum, which exhibits a spatially-dispersive profile. Furthermore, it is important to highlight that the cause of this phenomenon is the de Broglie-Proca mass term. We subsequently investigate the electromagnetic radiation emitted by a moving charged particle interacting with a medium for massless and massive non-linear electrodynamics. Our findings indicate that the radiation is driven by the medium through which the particle travels, similar to what is observed in the Cherenkov effect., Comment: 8 pages

We propose a Born-Infeld contribution to the $U(1)_{B-L}$ extension of the Standard Model to explain the anomalous decay of beryllium by the X17 neutral boson, its possible connections to dark matter and the observed MeV gamma-ray bursts. The decay width of the $Z^0$ decay into 3$X$ and 3$\gamma$ processes are computed, based on NA64 and ATLAS experiments data.

We examine the electromagnetic radiation produced by a moving charge in the QED vacuum that behaves as a dispersive medium characterized by a geometrical structure (discreteness/granularity) that emerges from loop quantum gravity. It is shown that the radiation is driven by the refractive vacuum the charged particle travels through reproducing the profile of the Cherenkov effect., Comment: 6 pages

We pursue the investigation of a generic non-linear extension of axionic electrodynamics in a Carroll-Field-Jackiw (CFJ) scenario that implements Lorentz-symmetry violation (LSV). The model we inspect consists of an arbitrary non-linear electrodynamic action coupled to the axion field in presence of an anisotropy four-vector that realizes the breaking of Lorentz symmetry under the particle point of view. The non-linear electromagnetic field is expanded around a constant and uniform magnetic background up to second order in the propagating photon field. The focus of our attention is the study of the material properties of the vacuum in the particular case of a space-like CFJ $4$-vector. The dispersion relations associated to the plane wave solutions are explicitly worked out in two situations: the magnetic background perpendicular and parallel to the wave direction. We extend these results to consider the analysis of the birefringence phenomenon in presence of non-linearity, the axion and the LSV manifested through the spatial anisotropy. Three specific proposals of non-linear electrodynamics are contemplated: Euler-Heisenberg, Born-Infeld and the Modified Maxwell electrodynamics. Throughout the paper, we shall justify why we follow the unusual path of connecting, in a single Lagrangian density, three pieces of physics beyond the Standard Model, namely, non-linearity, axions and LSV. Our true goal is to actually inspect and describe how axionic, non-linear and LSV effects interfere with one another whenever physical entities like group velocity, refraction indices, birefringence and effective masses of physical excitations are computed in presence of an external constant and homogeneous magnetic field., Comment: 33 pages, no figures, published version in JHEP

We propose and study the properties of a non-linear electrodynamics that emerges inspired on the physics of Dirac materials. This new electrodynamic model is an extension of the one-loop corrected non-linear effective Lagrangian computed in the work of ref. [3]. In the particular regime of a strong magnetic and a weak electric field, it reduces to the photonic non-linear model worked out by the authors of ref. [3]. We pursue our investigation of the proposed model by analyzing properties of the permittivity and permeability tensors, the energy-momentum tensor and wave propagation effects in presence of a uniform magnetic background. It is shown that the electrodynamics here presented exhibits the vacuum birefringence phenomenon. Subsequently, we calculate the lowest-order modifications to the interaction energy, considering still the presence of a uniform external magnetic field. Our analysis is carried out within the framework of the gauge-invariant but path-dependent variables formalism. The calculation reveals a screened Coulomb-like potential with an effective electric charge that runs with the external magnetic field but, as expected for Dirac-type materials, the screening disappears whenever the external magnetic field is switched off., Comment: 9 pages, 3 figures

The work aims effective and low-dimensional systems. Some different contexts involving gravitational and electromagnetic interactions are investigated. The electromagnetic one approaches bosonic and fermionic Effective Quantum Field Theories non-minimally coupled in three spacetime dimensions submitted to the expansion of Foldy-Wouthuysen Transformation, what generates (non-)relativistic corrections. A study of the effects of an external electromagnetic field derived from the Maxwell-Chern-Simons Electrodynamics on the obtained interactions are executed, as well as the impact produced by the dimensional reduction on expanded higher dimensional fermionic system in comparison to the low-dimensional one. In the scenario of gravitational effective model, scalar and fermionic particle scatterings reveal inter-particles interactions beyond monopole-monopole, leading to velocity and spin contributions, and the results are compared to a modified Electrodynamics effective model. A non-perturbative model resourcing to Casual Dynamics Triangulation data is adopted to serve as consistency check of the potentials resultants. Low-dimensional Maxwell-Higgs effective models with modified kinetic terms are studied, submitting them to a Bogomol'nyi prescription-type for calculation of inferior (non-trivial) bound energy and the self-dual equations. Vortex solutions for gauge field non-specified by an ansatz are achieved and their topological feature detailed.

The properties of the modified Maxwell electrodynamics (ModMax) are investigated in presence of external and uniform electric and magnetic fields. We expand the non-linear theory around an electromagnetic background up to second order in the propagating fields to obtain the permittivity and permeability tensors, dispersion relations, group velocity and refractive indices as functions of external fields. The case with perpendicular background fields is contemplated. The phenomenon of birefringence is discussed and the fundamental role of the ModMax parameter becomes clear. We calculate the difference of the refractive indices in terms of this parameter and the external fields. Finally, we set up a scenario where the axion is present and compute the interaction energy for the coupled axion-ModMax electrodynamics if a magnetic background field is considered. This calculation is carried out in the framework of the gauge-invariant, but path-dependent variables formalism. Our results show that the interaction energy contains a linear component, leading to the confinement of static probe charges where the interference between the ModMax parameter, the axion mass and the axion-photon coupling constant is pointed out., Comment: 12 pages, 2 figures, published version in Physical Review D

The photon is the paradigm for a massless particle and current experimental tests set severe upper bounds on its mass. Probing such a small mass, or equivalently large Compton wavelength, is challenging at laboratory scales, but planetary or astrophysical phenomena may potentially reach much better sensitivities. In this work we consider the effect of a finite photon mass on Schumann resonances in the Earth-ionosphere cavity, since the TM modes circulating Earth have eigen-frequencies of order $\mathcal{O} (10 \, {\rm Hz})$ that could be sensitive to $m_\gamma \approx 10^{-14} \, {\rm eV/c}^2$. In particular, we update the limit from Kroll [Phys. Rev. Lett. 27, 340 (1971)], $m_\gamma \leq 2.4 \times 10^{-13} \, {\rm eV/c}^2$, by considering realistic conductivity profiles for the atmosphere. We find the conservative upper bound $m_\gamma \leq 2.5 \times 10^{-14} \, {\rm eV/c}^2$, a factor 9.6 more strict than Kroll's earlier projection., Comment: 7+2 pages, 3 figures. Matches published version

In this contribution, our efforts consist in presenting and discussing the status of a paper in progress we are working on to investigate how non-linear electromagnetic effects couple to the parameters that signal Lorentz-symmetry violation (LSV). Here, we realize LSV by means of a specific model, namely Carroll-Field-Jackiw's. We set the formulation by considering a general non-linear photonic Lagrangian (written in terms of the Lorentz-invariant bilinears in the field-strength) that may be coupled to different operators that carry the message of LSV. In possess of the polynomial equation expressing the dispersion relation and the refractive index, one can find the results that express how the (meta)material constitutive properties of the vacuum are affected by the mixing of the parameters that measure LSV with the parameters of the specific non-linear electrodynamic model under consideration. We expect that our efforts might be of interest in connection with the experiments carried out with the existing super-intense LASERs based on chirped pulse amplification., Comment: 8 pages, no figures, Presented at the Ninth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, May 17-26, 2022

In this contribution, we re-assess some aspects of axionic electrodynamics by coupling non-linear electromagnetic effects to axion physics. We present a number of motivations to justify the coupling of the axion to the photon in terms of a general non-linear extension of the electromagnetic sector. Our emphasis in the paper relies on the investigation of the constitutive permittivity and permeability tensors, for which the axion contributes by introducing dependence on the frequency and wave vector of the propagating radiation. Also, we point out how the axion mass and the axion-photon-photon coupling constant contribute to a dispersive behavior of the electromagnetic waves, in contrast to what happens in the case of non-linear extensions, when effective refractive indices appear which depend only on the direction of the propagation with respect to the external fields. The axion changes this picture by yielding refractive indices with dependence on the wavelength. We apply our results to the special case of the (non-birefringent) Born-Infeld Electrodynamics and we show that it becomes birefringent whenever the axion is coupled. The paper is supplemented by an Appendix, where we follow our own path to approach the recent discussion on a controversy in the definition of the Poynting vector of axionic electrodynamics., Comment: 32 pages, no figures, published version in JHEP

We study some observational signatures of nonlinearities of the electromagnetic field. First to all we show the vital role played by nonlinearities in triggering a material behavior of the vacuum with $(\varepsilon > 0, \mu <0)$, which corresponds to a ferrimagnetic material. Secondly, the permittivity and susceptibility induced by nonlinearities are considered in order to obtain the refractive index via the dispersion relation for logarithmic electrodynamics. Finally, we consider the electromagnetic radiation produced by a moving charged particle interacting with a medium characterized by nonlinearities of the electromagnetic field. To this end we consider logarithmic electrodynamics. The result shows that the radiation is driven by the medium through which the particle travels like the one that happens in the Cherenkov effect., Comment: 8 pages

We write down an $\mathcal{N}=1$ supersymmetric extension for non-Abelian gauge theories in (1+3) dimensions with a Lorentz- and CPT-violating term of the Carroll-Field-Jackiw type. By including effects of the background (supersymmetric) fermion bilinears that accompany Lorentz-symmetry violation in a Carroll-Field-Jackiw scenario, we investigate both the gauge boson and gaugino dispersion relations in order to compute their respective masses in terms of the background structures. Such results open up a potential path towards a possible mechanism for gaugino-gauge boson conversion, an analogue of the Primakoff effect, induced here not by an external magnetic field, but instead by the (Majorana) fermionic sector of the supersymmetry multiplet in the backstage of the Lorentz-symmetry violation., Comment: 21 pages, no figures. All the Sections have been highly improved. Results are unchanged and one appendix has been added. The accepted version in Physical Review D

In this work we perform a non-linear extension of the $U(1)_{\rm Y}$ sector of the Standard Model leading to novel quartic effective interactions between the neutral gauge bosons. We study the induced effects through high-energy processes resulting in three photons, namely, Z-boson decay and electron-positron annihilation. Available experimental data on these processes do not yield viable lower bounds on the mass parameter $\sqrt{\beta}$, but we estimate that the range $\sqrt{\beta} \lesssim m_Z$ could be reliably excluded with better statistics in future $e^- e^+$ colliders. We also discuss neutral gauge-boson scatterings, contextualizing our findings with recent results on anomalous quartic gauge couplings., Comment: 16 pages, 5 figures. The title has been changed, section 3C improved, results unchanged. Matches published version

We investigate the effects of the Born-Infeld action on the Abelian sector of the electroweak model. The consequence of this approach is the emergence of anomalous couplings in the neutral sector of the $Z$-gauge boson and photon. These new couplings consist of quartic interactions of the photon with the $Z$-particle, as for example, three-photon-and-one-$Z$ vertex. With that, we obtain the decay width of $Z \to 3\,\gamma$ from which we impose a bound on the Born-Infeld parameter. Other bounds are also obtained from the photon quartic couplings. Subsequently, we consider the presence of an external uniform magnetic field in connection with this Born-Infeld weak hypercharge model. The magnetic background field yields new kinematic effects, like the kinetic mixing between the photon and the $Z$-boson, and we obtain thereby the corresponding dispersion relations for the mixed photon-$Z$-particle system. Finally, we calculate the lowest-order modifications to the interaction energy for the anomalous coupling $3\gamma-Z$, within the framework of the gauge-invariant but path-dependent variables formalism. Our results show that the interaction energy contains a linear term leading to the confinement of static probe charges. With the help of the potential that comes out, interparticle forces are estimated., Comment: 11 pages, no figures, version published in the EPJC

We present a finite-energy electroweak-monopole solution obtained by considering non-linear extensions of the hypercharge sector of the Electroweak Theory, based on logarithmic and exponential versions of electrodynamics. We find constraints for a class of non-linear extensions and also work out an estimate for the monopole mass in this scenario. We finally derive a lower bound for the energy of the monopole and discuss the simpler case of a Dirac magnetic charge., Comment: 8 pages, published in EPJC

We study a Lorentz invariance violating extension for the pure photonic sector of the standard model in a supersymmetric scenario. We identify a number of independent background fermion condensates. An effective photonic action is proposed which is induced by the SUSY background fermion condensates. The physical consequences leading to direct measurable effects over the screening and confining properties are considered. In the specific case of the Carroll-Field-Jackiw, we pay special attention in analyzing the dispersion relations to derive the photon and photino masses in terms of the supersymmetric background parameters. In connection with astrophysical aspects of Lorentz-symmetry violation, we discuss the time delay between electromagnetic waves of different frequencies as a consequence of the appearance of the massive photon. We also point out that, in the scenario we propose to accommodate Lorentz-symmetry violation in presence of a supersymmetric background, there is room for a sort of fermionic Primakoff effect in which a photino-photon conversion may be induced by the fermionic sector of the supersymmetric background., Comment: 25 pages. This work has been submitted for publication in the Special Issue, "Lorentz Violation in Astroparticles and Gravitational Waves", of Galaxies

Non-linear electrodynamic models are re-assessed in this paper to pursue an investigation of the kinematics of the Compton effect in a magnetic background. Before considering specific models, we start off by presenting a general non-linear Lagrangian built up in terms of the most general Lorentz- and gauge-invariant combinations of the electric and magnetic fields. The extended Maxwell-like equations and the energy-momentum tensor conservation are presented and discussed in their generality. We next expand the fields around a uniform and time-independent electric and magnetic backgrounds up to second order in the propagating wave, and compute dispersion relations which account for the effect of the external fields. We obtain thereby the refraction index and the group velocity for the propagating radiation in different situations. In particular, we focus on the kinematics of the Compton effect in presence of external magnetic fields. This yields constraints that relate the derivatives of the general Lagrangian with respect to the field invariants and the magnetic background under consideration. We carry out our inspection by focusing on some specific non-linear electrodynamic effective models: Hoffmann-Infeld, Euler-Heisenberg, generalized Born-Infeld and Logarithmic., Comment: 13 pages, 9 figures, accepted version in Physical Review D

We address the effect of an anomalous triple gauge boson couplings on a physical observable for the electroweak sector of the Standard Model, when the $SU(2)_{L}\otimes U(1)_{Y}$ symmetry is spontaneously broken by the Higgs mechanism to $U(1)_{em}$. Our calculation is done within the framework of the gauge-invariant, but path-dependent variable formalism which is alternative to the Wilson loop approach. Our result shows that the interaction energy is the sum of a Yukawa and a linear potential, leading to the confinement of static probe charges. The point we wish to emphasize, however, is that the anomalous triple gauge boson couplings ($Z \gamma \gamma$) contributes to the confinement for distances on the intranuclear scale., Comment: 5 pages

In this work we analyse a non-minimal Lorentz-violating extension of the electroweak theory in the fermionic sector. Firstly we analyse the relation between the CKM rotation in the quark sector and possible contributions of this new coupling to flavour changing neutral currents (FCNC) processes. In sequel we look for non-diagonal terms through possible leptonic flavour violation (LFV) decays. Strong bounds are presented to the Lorentz violating parameters of both the quark and the leptonic sectors., Comment: Published version

Our contribution sets out to investigate the GeV-scale phenomenology of a model based on an $SU_{L}(2) \times U_{Y}(1) \times U(1)_{X}$-gauge symmetry. The model accommodates, as a consequence of the symmetry-breaking pattern, a light gauge boson at the GeV-scale or below, allowing then to set up a new low energy physics. The fermion sector includes an exotic candidate to Dark Matter (DM) and the whole fermionic field content yields, as it is mandatory, the cancellation of the chiral anomaly. %In this strict sense, we refer to our proposal as a unified description : two different and exclusive symmetry-breaking patterns are treated with a single Lagrangian density and a common symmetry group. Furthermore, The light gauge boson and the exotic fermion are proposed as candidates to the so-called dark sector of the model that we try to describe in this contribution. The low-energy spectrum exhibits a hidden scalar field with mass fixed at the GeV level in the Higgs sector. We calculate the DM relic density associated with the dark fermion candidate by considering two annihilation processes in which the light gauge boson works as a portal for the DM detection. The observed relic density points to a mass of $3.4$ GeV for the DM fermion, while the light gauge boson mass is $8.0$ GeV. We also investigate the direct detection of DM in the low energy regime and obtain the region of parameters allowed by recent discussions on DM limits. Finally, the correction to the muon magnetic dipole moment is calculated considering the gauge boson mass at the GeV scale or below., Comment: 17 pages, 5 figures

A minimal extension of the left-right symmetric model for neutrino masses that includes a vector-like singlet fermion dark matter (DM) is presented with the DM connected to the visible sector via a gauged U(1) portal. We discuss the symmetry breaking in this model and calculate the mass and mixings of the extra heavy neutral gauge boson at the TeV scale. The extra gauge boson can decay to both standard model particles as well to dark matter. We calculate the relic density of the singlet fermion dark matter and its direct detection cross section and use these constraints to obtain the allowed parameter range for the new gauge coupling and the dark matter mass., Comment: 19 pages, 8 figures

Our contribution sets out to investigate the phenomenology of a gauge model based on an $SU_{L}(2) \times U_{R}(1)_{Q} \times U(1)_{Q'}$-symmetry group. The model can accommodate, through its symmetry-breaking pattern, a candidate to a heavy $Z'$-boson at the TeV-scale. The extended Higgs sector introduces a heavy scalar whose mass lies in the region $1.2-3.7 \, \mbox{TeV}$. The fermion sector includes an exotic candidate to Dark Matter that mixes with the right-handed neutrino component in the Higgs sector, so that the whole field content ensures the cancellation of the $U(1)$-quiral anomaly. The masses are fixed according to the particular way the symmetry breaking takes place. In view of the possible symmetry breakdown pattern, we study the phenomenological implications in a high-energy scenario. We worek out the magnetic dipole momentum (MDM) of the exotic fermion and the transition MDM due to its mixing with the right-neutrino., Comment: 12 pages, 7 figures, 1 table

The excitations referred to as oscillons are long-lived time-dependent field configurations which emerge dynamically from non-linear field theories. Such long-lived solutions are of interest in applications that include systems of Condensed Matter Physics, the Standard Model of Particle Physics, Lorentz-symmetry violating scenarios and Cosmology. In this work, we show how oscillons may be accommodated in a supersymmetric scenario. We adopt as our framework simple ($\mathcal{N}=1$) supersymmetry in $D=1+1$ dimensions. We focus on the bosonic sector with oscillon configurations and their (classical) effects on the corresponding fermionic modes, (supersymmetric) partners of the oscillons. The particular model we adopt to pursue our investigation displays cubic self-interactions in the scalar sector.

Based on recent discussions on the so-called unconventional supersymmetry, we propose a 5D Chern-Simons AdS-$\mathcal{N}$-SUGRA formulation without gravitino fields and show that a residual local SUSY is preserved. We explore the properties of CS theories to find a solution to the field equations in a 5D manifold. With a Randall-Sundrum-type ansatz, we show that this particular dimensional reduction is compatible with SUSY, and some classes of 4D solutions are then analyzed., Comment: Some references were added

This work sets out to compute and discuss effects of spin, velocity and dimensionality on inter-particle potentials systematically derived from gauge field-theoretic models. We investigate the interaction of fermionic particles by the exchange of a vector field in a parity-preserving description in five-dimensional $(5D)$ space-time. A particular dimensional reduction prescription is adopted $-$ reduction by dimensional restriction $-$ and special effects, like a pseudo-spin dependence, show up in four dimensions $(4D)$. What we refer to as pseudo-spin shall be duly explained. The main idea we try to convey is that the calculation of the potentials in $5D$ and the consequent reduction to $4D$ exhibits new effects that are not present if the potential is calculated in $4D$ after the action has been reduced., Comment: In this version, new comments and results have been added in Sections IV, V and Concluding Comments. To be published in Phys. Rev. D

We have recently presented an extension of the standard variational calculus to include the presence of deformed derivatives in the Lagrangian of a system of particles and in the Lagrangian density of field-theoretic models. Classical Euler-Lagrange equations and the Hamiltonian formalism have been re-assessed in this approach. Whenever applied to a number of physical systems, the resulting dynamical equations come out to be the correct ones found in the literature, specially with mass-dependent and with non-linear equations for classical and quantum-mechanical systems. In the present contribution, we extend the variational approach with the intervalar form of deformed derivatives to study higher-order dissipative systems, with application to concrete situations, such as an accelerated point charge - this is the problem of the Abraham-Lorentz-Dirac force - to stochastic dynamics like the Langevin, the advection-convection-reaction and Fokker-Planck equations, Korteweg-de Vries equation, Landau-Lifshits-Gilbert equation and the Caldirola-Kanai Hamiltonian. By considering these different applications, we show that the formulation investigated in this paper may be a simple and promising path for dealing with dissipative, non-linear and stochastic systems through the variational approach., Comment: 19 pages

We settle a result on generic exactness of SUSY in 3-D, and provide a mechanism of F-term spontaneous breaking of 3-D SUSY, with a different set of tools from those used by O'Raifeartaigh in his seminal work on 4-D SUSY. In our study, we use techniques of projective algebraic geometry so as to deal successfully with cubic hypersurfaces., Comment: Comments are welcome

In this contribution, it is our aim to show that the Chern-Simons terms of modified gravity can be understood as generated by the addition of a 3-dimensional algebraic manifold to an initial 11-dimensional space-time manifold; this builds up an 11+3-dimensional space-time. In this system, firstly, some fields living in the bulk join the fields that live on the 11-dimensional manifold, so that the rank of the gauge fields exceeds the dimension of the algebra; consequently, there emerges an anomaly. To solve this problem, another 11-dimensional manifold is included in the 11 +3-dimensional space-time, and it interacts with the initial manifold by exchanging Chern-Simons fields. This mechanism is able to remove the anomaly. Chern-Simons terms actually produce an extra manifold between the pair of 11-dimensional manifolds of the 11+3-space-time. Summing up over the topology of both the 11-dimensional manifolds and the topology of the exchanged Chern-Simons manifold in the bulk , we conclude that the total topology shrinks to one, which is in agreement with the main idea of the Big Bang theory., Comment: 11 pages, 2 figures

Our contribution sets out to investigate the phenomenology of a gauge model based on an $SU_{L}(2) \times U_{R}(1)_{J} \times U(1)_{K}$-symmetry group. The model can accommodate in its distinct phases - by virtue of different symmetry-breaking patterns - a candidate to a heavy $Z'$-boson at the TeV-scale and the recently discussed $17 \, \mbox{MeV}$ X-boson that may bring about a new physics at the $\mbox{MeV}$-scale. Furthermore, the para-photon of the dark matter sector and the candidate to the so-called dark photon can also be described in the scenario we are endeavoring to set up in this paper. In the $Z'$-scenario, the extended Higgs sector introduces a heavy scalar whose mass lies in the region $1.2-3.7 \, \mbox{TeV}$, while that the lower energy scale scenario presents a light scalar with mass in the interval $1.9-19 \, \mbox{GeV}$. The fermionic sector includes an exotic candidate to dark matter that mixes with the right-neutrino component in the Higgs sector, so that the whole field content yields the cancellation of the U(1)-anomaly. The masses are fixed according to the particular way the symmetry breaking takes place. In view of the possible symmetry breakdown patterns, we study the phenomenological implications in both scenarios of high- and low-energy scales. As examples, we consider the scattering of Standard Model matter into dark sector constituents intermediated by the $Z'$-boson in the $\mbox{TeV}$-scale, and the corresponding scattering intermediated by a lightest boson in the lower scale physics. Furthermore, we obtain the magnetic dipole momentum (MDM) of the exotic fermion and the transition MDM due to the mixing with the right-neutrino., Comment: 38 pages, 13 figures

The standard electroweak interaction is here re-assessed to accommodate two different situations in Particle Physics. The first one is a $Z'$-model at the TeV-scale physics. The second one tackles the recent discussion of a possible fifth force mediated by a $17$-MeV X-boson associated with an electron-positron emission in the transition of an excited 8-Beryllium to its ground state. The anomaly-free model that provides these two scenarios is based on an $SU_{L}(2) \times U_{R}(1)_{J} \times U(1)_{K}$-symmetry. It yields a new massive neutral boson, an exotic massive neutral fermion, right-neutrinos and an additional neutral Higgs particle, which stems from a supplementary Higgs field, introduced along with the usual Higgs doublet responsible for the electroweak breaking and the masses of $W^{\pm}$ and $Z^{0}$. Yukawa interactions of the two scalars generate the masses of the Standard Model leptons, neutrinos and a new exotic fermion of the model. The vacuum expectation values of the Higgses fix up two independent energy scales. One of them is the well-confirmed electroweak scale, $246 \, \mbox{GeV}$, whereas the other one is set up by adopting an experimental estimate for the $Z'$-mass., Comment: 11 pages, 2 figures

In this contribution, we build up an axiomatic local metric derivative that exhibits the Mittag-Leffler as an eigenfunction and is valid for low-level fractionality, whenever the order parameter is close to $1$. This version of deformed or metric derivative may be a possible alternative to the versions by Jumarie and the inappropriately so-called local fractional derivative also based on the Jumarie's approach. With rules similar to the classical ones, but with a solid axiomatic basis in the limit pointed out here, we present our results and some comments on the limits of validity for the controversial formalism found in the literature of the area., Comment: 5 pages

By the thermofield dynamics (TFD) formalism we obtain the energy-momentum tensor for the Electromagnetism with Lorentz Breaking Even term of the Standard Model Extended (SME) Sector in a topology $S^{1}\times S^{1}\times R^{2}$. We carry out the compactification by a generalized TFD-Bogoliubov transformation that is used to define a renormalized energy-momentum tensor, and the Casimir energy and pressure at finite temperature are then derived. A comparative analysis with the electromagnetic case is developed, and we remark the influence of the background in the traditional Casimir effect., Comment: 19 pages. arXiv admin note: substantial text overlap with arXiv:1012.0352

This paper sets out to establish a comparative study between classes of spin- and velocity-dependent potentials for spin-1/2 and spin-1 matter currents/sources in the non-relativistic regime. Both (neutral massive) scalar and vector particles are considered to mediate the interactions between (pseudo-)scalar sources or (pseudo-)vector currents. Though our discussion is more general, we contemplate specific cases in which our results may describe the electromagnetic interaction with a massive (Proca-type) photon exchanged between two spin-1/2 or two spin-1 carriers. We highlight the similarities and peculiarities of the potentials for the two different types of charged matter and also focus our attention on the comparison between the particular aspects of two different field representations for spin-1 matter particles. We believe that our results may contribute to a further discussion of the relation between charge, spin and extensibility of elementary particles., Comment: In this version (v5), a Corrigendum has been added after the published paper

We present an N=1 supersymmetric generalization of the Maximal Abelian Gauge (MAG) in its superfield and component-field formulations, and discuss its Faddeev-Popov quantization, the associated BRST symmetry and the corresponding Slavnov-Taylor identity in superspace approach., Comment: 11 pages, no figures

Over the recent decades, diverse formalisms have emerged that are adopted to approach complex systems. Amongst those, we may quote the q-calculus in Tsallis' version of Non-Extensive Statistics with its undeniable success whenever applied to a wide class of different systems; Kaniadakis' approach, based on the compatibility between relativity and thermodynamics; Fractional Calculus (FC), that deals with the dynamics of anomalous transport and other natural phenomena, and also some local versions of FC that claim to be able to study fractal and multifractal spaces and to describe dynamics in these spaces by means of fractional differential equations. The question we might ask is whether or not there are common aspects that connect these alternative approaches. In this short communication, we discuss a possible relationship between q-deformed algebras in two different contexts of Statistical Mechanics, namely, the Tsallis' framework and the Kaniadakis' scenario, with local form of fractional-derivative operators defined in fractal media, the so-called Hausdorff derivatives, mapped into a continuous medium with a fractal measure. This connection opens up new perspectives for theories that satisfactorily describe the dynamics for the transport in media with fractal metrics, such as porous or granular media. Possible connections with other alternative definitions of FC are also contempled. Insights on complexity connected to concepts like coarse-grained space-time and physics in general are pointed out., Comment: 12 pages. Original Article

Background fermion condensates in a landscape dominated by global SUSY are reassessed in connection with a scenario where Lorentz symmetry is violated in the bosonic sector (actually, the photon sector) by a $CPT$-even $k_F$-term. An effective photonic action is discussed that originates from the supersymmetric background fermion condensates. Also, the photino mass emerges in terms of a particular condensate contrary to what happens in the $k_{AF}$-violation. Finally, the interparticle potential induced by the effective photonic action is investigated and a confining profile is identified., Comment: 14 pages. arXiv admin note: text overlap with arXiv:1102.3777 by other authors

We investigate the role played by particular field representations of an intermediate massive spin-1 boson in the context of spin-dependent interparticle potentials between fermionic sources in the limit of low momentum transfer. The comparison between the well-known case of the Proca field and that of an exchanged spin-1 boson (with gauge-invariant mass) described by a 2-form potential mixed with a 4-vector gauge field is established in order to pursue an analysis of spin- as well as velocity-dependent profiles of the interparticle potentials. We discuss possible applications and derive an upper bound on the product of vector and pseudo-tensor coupling constants., Comment: 23 pages, 2 figures

This paper is devoted to investigating the interactions between stationary sources of the electromagnetic field, in a model which exhibits explicit Lorentz-symmetry breaking due to the presence of a single background vector. We focus on physical phenomena that emerge from this kind of breaking and which have no counterpart in Maxwell Electrodynamics.

We here propose a 5-dimensional {\bf Abelian gauge} model based on the mixing between a $U(1)$ potential and an Abelian 3-form field by means of a topological mass term. An extended covariant derivative is introduced to minimally couple a Dirac field to the $U(1)$ potential, while this same covariant derivative non-minimally couples the 3-form field to the charged fermion. A number of properties are discussed in 5D; in particular, the appearance of a topological fermionic current. A 4-dimensional reduced version of the model is investigated and, { \bf in addition to the $U(1)$ electric- and magnetic-sort of fields,} there emerges an extra set of electric- and magnetic-like fields which contribute a negative pressure and may be identified as a possible fraction of dark energy. The role of the topological fermionic current is also contemplated upon dimensional reduction from 5D to 4D. Other issues we present in 4 space-time dimensions are the emergence {\bf of a pseudo-scalar massive particle,} an extra massive neutral gauge boson,{\bf which we interpret as a kind of paraphoton}, and the calculation of spin- and velocity-dependent interparticle potentials associated to the exchange of the intermediate bosonic fields of the model., Comment: -- 30 pages -- L. P. R. Ospedal appears as a new co-author; modifications by inclusion of the gravitational sector and the attainment of a spin- and velocity-dependent potential as an application have been worked out in this Revised Version

In this work, we investigate aspects of the electron, muon and tau gyromagnetic ratios (g-factor) in a fractional coarse-grained scenario, by adopting a Modified Riemann-Liouville (MRL) fractional calculus. We point out the possibility of mapping the experimental values of the specie's g-factors into a theoretical parameter which accounts for fractionality, without computing higher-order QED calculations. We wish to understand whether the value of (g-2) may be traced back to a fractionality of space-time.The justification for the difference between the experimental and the theoretical value g=2 stemming from the Dirac equation is given in the terms of the complexity of the interactions of the charged leptons, considered as pseudo-particles and "dressed" by the interactions and the medium. Stepwise, we build up a fractional Dirac equation from the fractional Weyl equation that, on the other hand, was formulated exclusively in terms of the helicity operator. From the fractional angular momentum algebra, in a coarse-grained scenario, we work out the eigenvalues of the spin operator. Based on the standard electromagnetic current, as an analogy case, we write down a fractional Lagrangian density, with the electromagnetic field minimally coupled to the particular charged lepton. We then study a fractional gauge-like invariance symmetry, formulate the covariant fractional derivative and propose the spinor field transformation. Finally, by taking the non-relativistic regime of the fractional Dirac equation, the fractional Pauli equation is obtained and, from that, an explicit expression for the fractional g-factor comes out that is compared with the experimental CODATA value. Our claim is that the different lepton species must probe space-time by experiencing different fractionalities, once the latter may be associated to the effective interactions of the different families with the medium., Comment: 15 pages

We study the spectrum of the minimal supersymmetric extension of the Carroll-Field-Jackiw model for Electrodynamics with a topological Chern-Simons-like Lorentz-symmetry violating term. We identify a number of independent background fermion condensates, work out the gaugino dispersion relation and propose a photonic effective action to consider aspects of confinement induced by the SUSY background fermion condensates, which also appear to signal Lorentz-symmetry violation in the photino sector of the action. Our calculations of the static potential are carried out within the framework of the gauge-invariant but path-dependent variables formalism which are alternative to the Wilson loop approach. Our results show that the interaction energy contains a linear term leading to the confinement of static probe charges., Comment: 11 pages, photino dispersion relation is extended to included the case the photino acquires mass through spontaneous SUSY breaking

The hydrogen atom in two dimensions, described by a Schr\"odinger equation with a Chern-Simons potential, is numerically solved. Both its wave functions and eigenvalues were determined for small values of the principal quantum number $n$. The only possible states correspond to $l=0$. How the result depends on the topological mass of the photon is also discussed. In the case $n=1$, the energy of the fundamental state corresponding to different choice for the photon mass scale are found to be comprehended in the interval $-3,5 \times 10^{-3} eV \leq E \leq -9,0 \times 10^{-2} eV$, corresponding to a mean radius of the electron in the range $ (5.637 \pm 0.005) \times 10^{-8}$~cm $\leq \leq (48.87 \pm 0.03) \times 10^{-8}$~cm. In any case, the planar atom is found to be very weekly bounded showing some features similar to the Rydberg atoms in three dimensions with a Coulombian interaction., Comment: 6 pages, 5 figures

A new set of projection operators for three-dimensional models are constructed. Using these operators, an uncomplicated and easily handling algorithm for analysing the unitarity of the aforementioned systems is built up. Interestingly enough, this method converts the task of probing the unitarity of a given 3D system, that is in general a time-consuming work, into a straightforward algebraic exercise; besides, it also greatly clarifies the physical interpretation of the propagating modes. In order to test the efficacy and quickness of the algorithm at hand, the unitarity of some important and timely higher-order electromagnetic (gravitational) systems augmented by both Chern-Simons and higher order Chern-Simons terms are investigated., Comment: 14 pages. Matches published version

In this work, we adopt the simplest model that spontaneously breaks supersymmetry, namely, the minimal O'Raifeartaigh model. The effective potential is computed in the framework of the linear delta expansion (LDE) approach up to the order $\delta^2$, conjugated with superspace and supergraph techniques. The latter can be duly mastered even if supersymmetry is no longer exact and the efficacy of the superfield approach in connection with the LDE procedure is confirmed according to our investigation. That opens up a way for a semi-nonperturbative superspace computation which allows us to deal with spontaneously broken supersymmetric models and encourages us to go further and apply this treatment to the Minimal Supersymmetric Standard Model (MSSM) precision tests., Comment: 42 pages, 22 figures, text modified, new paragraph added in the conclusions, revtex4

The main goal of this paper is to set up the coarse-grained formulation of a fractional Schr\"odinger equation that incorporates a higher (spatial) derivative term which accounts for relativistic effects at a lowest order. The corresponding continuity equation is worked out and we also identify the contribution of the relativistic correction the quantum potential in the coarse-grained treatment. As a consequence, in the classical regime, we derive the sort of fractional Newtonian law with the quantum potential included and the fractional conterparts of the De Broglies's energy and momentum relations., Comment: 16 pages. to be submitted. Corrected

We study the dynamics of a charged spin-1/2 particle in an external 5-dimensional electromagnetic field. We then consider that we are at the $TeV$\ scale, so that we can access the fifth dimension and carry out our physical considerations in a 5-dimensional brane. In this brane, we focus our attention to the quantum-mechanical dynamics of a charged particle minimally coupled to the 5-dimensional electromagnetic field. We propose a way to identify the Abraham-Lorentz back reaction force as an effect of the extra (fifth) dimension. Also, a sort of dark matter behavior can be identified in a particular regime of the dynamics of the particle interacting with the bulk electric field., Comment: 8 pages

We adopt a superspace/supergraph formalism to pursue the investigation of the structure of one- and two-loop divergences in the frame of the minimal O'Raifeartaigh model that realizes the F-term spontaneous supersymmetry breaking. The linear delta expansion(LDE) procedure is introduced and renormalization is carried out up to the second order in the LDE expansion parameter. In agreement with the nonrenormalization theorem for the (chiral/antichiral) matter potential of ${\mathcal N}=1, \ D=4$ supersymmetry, our explicit supergraph calculations confirm that only the K\"{a}hler potential is actually renomalized., Comment: 23 pages, 4 figures, revtex4. arXiv admin note: text overlap with arXiv:0904.4672